Integration

Question

How do I solve this? iv have gotten like 3 different answers.

Evaluate the following expression by writing it as a definite integral. lim x→∞ ∑ⁿ _k=1 [4+(2k/n)]² (2/n)

Answer 1

Remember what you are trying to do here is convert a Riemann sum into it's integral counterpart.

 

i.e.  lim _n→∞Σⁿ_k=1 [f(x + kΔx)]Δx where Δx = (b-a)/n    i.e. over the interval (a,b)

 

In your question I will start you off by pointing out the leftmost (k=1) value of x over the interval is 4 + (2/n). This gives you the value of a.

 

Can you do the rest?

 

If not comment back.